03568nam a22005175i 4500 978-3-031-48158-1 DE-He213 20251030112656.0 cr nn 008mamaa 240729s2024 sz | s |||| 0|eng d 9783031481581 978-3-031-48158-1 10.1007/978-3-031-48158-1 doi Q124.6-127.2 PDX bicssc SCI034000 bisacsh PDX thema Høyrup, Jens. author. aut http://id.loc.gov/vocabulary/relators/aut 73952 Explorations and False Trails [electronic resource] : The Innovative Techniques That Brought About Modern Algebra / by Jens Høyrup. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 143 p. 15 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs in History of Science and Technology, 2211-4572 Preface -- Introduction -- Chapter 1. Geometric proofs -- Chapter 2. Powers of the unknown -- Chapter 3. Abbreviations, glyphs, symbols and symbolic calculation -- Chapter 4. Embedding and parenthesis function -- Chapter 5. Several unknowns -- Chapter 6. The transition to incipient modern algebra -- Bibliography -- Index. . This book provides a unique perspective on the history of European algebra up to the advent of Viète and Descartes. The standard version of this history is written on the basis of a narrow and misleading source basis: the Latin translations of al-Khwārizmī, Fibonacci's Liber abbaci, Luca Pacioli's Summa, Cardano's Ars magna—with neither Fibonacci nor Pacioli being read in detail. The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Viète's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps. This book traces the meandering development of all these techniques along with the mostly ignored but very important parenthesis function, by means of detailed readings of all pertinent sources, including the abacus and cossic algebra and French algebra from Chuquet to Gosselin. It argues for a necessary distinction between abbreviating glyphs and genuine symbols serving within a symbolic syntax, which allows it to trace the emergence of symbolic calculation. Characterization of the mathematical practice of the environment within which Viète and Descartes moved allows for an explanation of how these two figures did not even need to invent abstract coefficients but rather received them as a gift. Science History. 65232 Mathematics. 65523 History. History of Science. 66101 History of Mathematical Sciences. 66197 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031481574 Printed edition: 9783031481598 SpringerBriefs in History of Science and Technology, 2211-4572 80976 https://doi.org/10.1007/978-3-031-48158-1 ZDB-2-HTY ZDB-2-SXH 62006 62006